I've grown trays and trays of this stuff. Here's what works for me...
Get an undrained 1020 tray (I like
these but any thing undrained and at least 3" deep will work) and lay in about 1" of moistened dead sphagnum. Put your live sphagnum on top of this and press it in so it has good contact with the dead stuff. Keep the live sphagnum moist while still exposed to the air and put it in the strongest light you possibly can while also not letting it dry out.
The dead stuff can be sitting in water as long as the live stuff is above the waterline. The important thing to remember is that most mosses (including sphagnum) are land plants that lack a vascular system so they need access to
both water and oxygen at all times. If the sphagnum is submerged or otherwise unable to obtain enough oxygen, growth will slow dramatically.
On the other end of the spectrum, I've found that sphagnum is also very drought resistant and I've had trays full of white, crispy bone dry moss that greened up and started growing again after giving them some water. I'd definitely avoid allowing the moss to dry out but don't panic it happens. Just give it some good, clean water and it should be back to the races.
I'd strongly consider stopping the fertilizer since I've found that just encourages algae and other rival moss growth. I typically don't fertilize mine at all and they grow very well. I have, however, noticed problems with algae when I did fertilize and so steer clear of it now. Focus on the basics of water, light, air, and temp and you'll soon have bunches of the stuff.
If you insist on fertilizing then I'd start out with a super light dose ... ~1/10 strength and adjust from there. You want just enough nutrients to benefit the moss without providing any benefits to anyone else.
In terms of light, I've found that sphagnum grows best when it's gets tons of sun. Some people have reported that it grows best in partial sun or shade but I think that's because it's easier to keep moist under those conditions and in that situation, shade is the lesser of 2 evils. Or maybe it's because the moss will grow longer (etoliate) trying to reach more light but I've found this growth to be weaker and less vigorous. The ideal situation I've found is keeping the moss moist while giving it as much light as possible. Seriously, this stuff will take 12 hours of full sun as long as you can prevent it from drying out ... and turn beautiful shades of red, yellow, orange as well.
In terms of temps, it seems to like it mild with ~70F days and cooler nights. For me here in North Carolina, it grows best in the spring and fall but slows down to a crawl in the cold winter and hot summer. Even under good conditions though, we're probably talking about just a few inches of growth per year so don't expect it to take over your backyard anytime soon.
Oh, one other tip is that it seems to like growing in clumps
much more than growing alone. I'm not sure if this is because it creates its own microclimate or for some other reason but I've noticed that it is much happier when bunched up together.
Or you could just press the easy button and just put it in the tops of your sarracenia pots. They like the same conditions so should grow very well there. I do this and have so much growing in my sarracenia pots that I don't really bother with the trays any more.
Hope that helps!